Three numbers are in the ratio 2 : 3 : 4, If their LCM is 240 the smaller of the three numbers is = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let number are}} \cr & {\text{ = }}2x,3x,4x \cr & {\text{given,}} \cr & {\text{LCM of }}\left( {2 \times 3 \times 4} \right)x = 24x \cr & 24x = 240 \cr & x = 10 \cr & \therefore {\text{numbers are 2}} \times {\text{10 = 20}} \cr & {\text{3}} \times 10 = 30 \cr & {\text{4}} \times 10 = 40 \cr & \therefore {\text{Smaller is 20}} \cr} $$